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## Topic: lambda calculus

topics > Group: mathematics

Topic:
curried functions
Topic:
formal methods and languages
Topic:
function application
Topic:
functional programming
Topic:
logic programming
Topic:
programming as mathematics
Topic:
recursion
Topic:
reduction languages
Topic:
reduction machines
Topic:
type algebras, typed lambda calculus, and type-complete languages
Subtopic: lambda operator and free variables

 Quote: generalization is the same as the abstraction or lambda operator in symbolic logic [»kimuTD7_1985] Quote: a form is a meaningful expression with free variables Quote: a form has a value for every system of admissible values of its free variables [»churA_1951] Quote: assume unambiguous concepts, unambiguous constants, the free variables of a form determine its sense-value [»churA_1951] Quote: LINQ infers IEnumerable from a select expression; it compiles with a lambda expression [»bierGM10_2007]

Subtopic: bound vs. free variable

 Quote: a bound variable or parameter is symbol independent, while a free variable depends on context [»landPJ_1966, OK]

Subtopic: reduction

 Quote: reduction is the atom of behavior of lambda-calculus; i.e., passing an argument to a function Quote: reduction in lambda calculus is like eliminating differentiation in the differential calculus [»wegnP10_1986]

Subtopic: objects vs. values

 Quote: a theory of objects as a foundation for object-oriented programming; like lambda calculus but based on objects as primitives; handles classes, self, dynamic dispatch, inheritance, etc. [»abadM_1996]

Subtopic: petri nets

 Quote: combine Petri net theory with a compositional view of systems; like combining Turing machines with lambda-calculus [»milnR1_1993]

Subtopic: examples

 Quote: an expression tree, Expression, is an efficient, in-memory representation of a lambda expression; LINC translates expression trees into SQL [»bierGM10_2007] QuoteRef: leavBM4_1970 ;; an implementation of lambda calculus Quote: create a library of useful subroutines; a calculus of instructions [»maucJW1_1947] Quote: an applicative expression consists of lambda expressions, operator applications, and expression lists; a fundamental notation [»landPJ1_1964]

Subtopic: limitations of lambda calculus

 Quote: because of self-reference, could not construct a set-theoretic model of the .lambda.-calculus Quote: in type-free, lambda calculus, can not define a universal domain that includes all functions [»straC3_1973]

Related Topics

Topic: curried functions (14 items)
Topic: formal methods and languages (53 items)
Topic: function application (18 items)
Topic: functional programming (45 items)
Topic: logic programming (34 items)
Topic: programming as mathematics (27 items)
Topic: recursion (16 items)
Topic: reduction languages (17 items)
Topic: reduction machines (14 items)
Topic: type algebras, typed lambda calculus, and type-complete languages
(28 items)

Updated barberCB 7/04